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  2. Irrational number - Wikipedia

    en.wikipedia.org/wiki/Irrational_number

    An example of an irrational algebraic number is x 0 = (2 1/2 + 1) 1/3. ... so it is not true that every real number is rational or irrational. Thus, the notion of an ...

  3. List of types of numbers - Wikipedia

    en.wikipedia.org/wiki/List_of_types_of_numbers

    All integers are rational, but there are rational numbers that are not integers, such as −2/9. Real numbers (): Numbers that correspond to points along a line. They can be positive, negative, or zero. All rational numbers are real, but the converse is not true. Irrational numbers (): Real numbers that are not rational.

  4. Square root of 2 - Wikipedia

    en.wikipedia.org/wiki/Square_root_of_2

    The square root of 2 (approximately 1.4142) is the positive real number that, when multiplied by itself or squared, equals the number 2. It may be written in mathematics as 2 {\displaystyle {\sqrt {2}}} or 2 1 / 2 {\displaystyle 2^{1/2}} .

  5. Category:Irrational numbers - Wikipedia

    en.wikipedia.org/wiki/Category:Irrational_numbers

    In mathematics, an irrational number is any real number that is not a rational number, i.e., one that cannot be written as a fraction a / b with a and b integers and b not zero. This is also known as being incommensurable, or without common measure. The irrational numbers are precisely those numbers whose expansion in any given base (decimal ...

  6. Dirichlet function - Wikipedia

    en.wikipedia.org/wiki/Dirichlet_function

    Again, we can take ε = 12, and this time, because the rational numbers are dense in the reals, we can pick z to be a rational number as close to y as is required. Again, f ( z ) = 1 is more than 12 away from f ( y ) = 0 .

  7. Irrationality measure - Wikipedia

    en.wikipedia.org/wiki/Irrationality_measure

    Rational numbers have irrationality exponent 1, while (as a consequence of Dirichlet's approximation theorem) every irrational number has irrationality exponent at least 2. On the other hand, an application of Borel-Cantelli lemma shows that almost all numbers, including all algebraic irrational numbers , have an irrationality exponent exactly ...

  8. Rational number - Wikipedia

    en.wikipedia.org/wiki/Rational_number

    In mathematics, "rational" is often used as a noun abbreviating "rational number". The adjective rational sometimes means that the coefficients are rational numbers. For example, a rational point is a point with rational coordinates (i.e., a point whose coordinates are rational numbers); a rational matrix is a matrix of rational numbers; a rational polynomial may be a polynomial with rational ...

  9. Repeating decimal - Wikipedia

    en.wikipedia.org/wiki/Repeating_decimal

    Examples of such irrational numbers are √ 2 ... of ⁠ 1 / p ⁠, we can check whether the ... there is 0. 1 = 1. T = ⁠ 1 / 2 ⁠. A rational number has an ...